The light gathering power of a telescope/camera is proportional to the area of its aperture. So the Earth telescope has 2500x the power of the larger New Horizons camera. But light decreases as the square of distance – so New Horizon needs to be 1/50th as far from the KBO as Earth. Note, the “squares cancel” and the relative distance is proportional to the lens aperture.

For example, if the hypothetical Planet X is ~50 billion miles from the sun, New Horizons would have to be within 1 billion miles of it.